Abstract

We conducted a numerical study to investigate the minimum modulation depth of a saturable absorber that is essentially required for stable optical pulses to be generated from a passively mode-locked fiber laser cavity. More specifically, an extended nonlinear Schrödinger equation was numerically solved in order to analyze the impact of the cavity group velocity dispersion (GVD), cavity χ(3) nonlinearity, and saturation gain of an active fiber on the minimum modulation depth that is required. The net cavity GVD is shown to significantly influence the required minimum modulation depth level of a saturable absorber. A cavity with little net anomalous dispersion was found to be readily mode locked through the use of a saturable absorber with a very small amount of modulation depth. Furthermore, the reason that a fiber laser cavity with a zero cavity GVD becomes unstable and needs a much higher modulation depth was investigated, and such a condition was found to be associated with the fiber χ(3) nonlinearity. The minimum modulation depth was also shown to vary according to the saturation gain level of an active fiber.

© 2014 Optical Society of America

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    [Crossref]
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2014 (6)

S. Y. Choi, H. Jeong, B. H. Hong, F. Rotermund, and D.-I. Yeom, “All-fiber dissipative soliton laser with 10.2  nJ pulse energy using an evanescent field interaction with graphene saturable absorber,” Laser Phys. Lett. 11, 015101 (2014).
[Crossref]

J. Lee, J. Koo, Y. M. Jhon, and J. H. Lee, “A femtosecond pulse erbium fiber laser incorporating a saturable absorber based on bulk-structured Bi2Te3 topological insulator,” Opt. Express 22, 6156–6173 (2014).

Y.-H. Lin, C.-Y. Yang, S.-F. Lin, W.-H. Tseng, Q. Bao, C.-I. Wu, and G. R. Lin, “Soliton compression of the erbium-doped fiber laser weakly started mode-locking by nanoscale p-type Bi2Te3 topological insulator particles,” Laser Phys. Lett. 11, 055107 (2014).
[Crossref]

J. Sotor, G. Sobon, W. Marcherzynski, P. Paletko, K. Grodecki, and K. M. Abramski, “Mode-locking in Er-doped fiber laser based on mechanically exfoliated Sb2Te3 saturable absorber,” Opt. Mater. Express 4, 1–6 (2014).
[Crossref]

H. H. Liu and K. K. Chow, “Enhanced stability of dispersion-managed mode-locked fiber lasers with near-zero net cavity GVD by high-contrast saturable absorbers,” Opt. Lett. 39, 150–153 (2014).
[Crossref]

M. Jung, J. Lee, J. Koo, J. Park, Y.-W. Song, K. Lee, S. Lee, and J. H. Lee, “A femtosecond pulse fiber laser at 1935  nm using a bulk-structured Bi2Te3 topological insulator,” Opt. Express 22, 7865–7874 (2014).
[Crossref]

2013 (2)

Y. Chen, C. Zhao, H. Huang, S. Chen, P. Tang, Z. Wang, S. Lu, H. Zhang, S. Wen, and D. Tang, “Self-assembled topological insulator: Bi2Se3 membrane as a passive Q-switcher in an erbium-doped fiber laser,” J. Lightwave Technol. 31, 2857–2863 (2013).
[Crossref]

J. Lee, J. Koo, P. Debnath, Y.-W. Song, and J. H. Lee, “A Q-switched, mode-locked fiber laser using a graphene oxide-based polarization sensitive saturable absorber,” Laser Phys. Lett. 10, 035103 (2013).
[Crossref]

2012 (5)

S. K. Truitsyn, B. G. Bale, and M. P. Fedoruk, “Dispersion-managed solitons in fibre systems and lasers,” Phys. Rep. 521, 135–203 (2012).
[Crossref]

C. Zhao, Y. Zou, Y. Chen, Z. Wang, S. Lu, H. Zhang, S. Wen, and D. Tang, “Wavelength-tunable picosecond soliton fiber laser with topological insulator: Bi2Se3 as a mode locker,” Opt. Express 20, 27888–27895 (2012).
[Crossref]

A. Martinez and S. Yamashita, “10  GHz fundamental mode fiber laser using a graphene saturable absorber,” Appl. Phys. Lett. 101, 041118 (2012).
[Crossref]

Y. M. Chang, J. Lee, and J. H. Lee, “Active mode-locking of an erbium-doped fiber laser using an ultrafast silicon-based variable optical attenuator,” Jpn. J. Appl. Phys. 51, 072701 (2012).

Z. Sun, T. Hasan, and A. C. Ferrari, “Ultrafast lasers mode-locked by nanotubes and graphene,” Physica E 44, 1082–1091 (2012).
[Crossref]

2011 (4)

2010 (4)

Y.-W. Song, S.-Y. Jang, W.-S. Han, and M.-K. Bae, “Graphene mode-lockers for fiber lasers functioned with evanescent field interaction,” Appl. Phys. Lett. 96, 051122 (2010).
[Crossref]

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4, 803–810 (2010).
[Crossref]

Y. M. Chang, H. Kim, J. H. Lee, and Y.-W. Song, “Multilayered graphene efficiently formed by mechanical exfoliation for nonlinear saturable absorbers in fiber mode-locked lasers,” Appl. Phys. Lett. 97, 211102 (2010).
[Crossref]

D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives,” J. Opt. Soc. Am. B 27, 63–92 (2010).

2009 (2)

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. Shen, K. P. Loh, and D. Y. Tang, “Atomic layer graphene as saturable absorber for ultrafast pulsed laser,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

O. Shtyrina, M. Fedoruk, S. Turitsyn, R. Herda, and O. Okhotnikov, “Evolution and stability of pulse regimes in SESAM-mode-locked femtosecond fiber lasers,” J. Opt. Soc. Am. B 26, 346–352 (2009).
[Crossref]

2008 (1)

2006 (1)

2004 (2)

S. Y. Set, H. Yaguchi, Y. Tanaka, and M. Jablonski, “Laser mode locking using a saturable absorber incorporating carbon nanotubes,” J. Lightwave Technol. 22, 51–56 (2004).
[Crossref]

H. Haiml, R. Grange, and U. Keller, “Optical characterization of semiconductor saturable absorbers,” Appl. Phys. B 79, 331–339 (2004).
[Crossref]

2001 (1)

2000 (3)

K. Song and M. Premaratne, “Effects of SPM, XPM, and four-wave-mixing in L-band EDFAs on fiber-optic signal transmission,” IEEE Photon. Technol. Lett. 12, 1630–1632 (2000).
[Crossref]

H. A. Haus, “Mode-locking of lasers,” IEEE J. Quantum Electron. 6, 1173–1185 (2000).
[Crossref]

C. Wu and N. K. Dutta, “High-repetition-rate optical pulse generation using a rational harmonic mode-locked fiber laser,” IEEE J. Quantum Electron. 36, 145–150 (2000).
[Crossref]

1999 (1)

1998 (2)

M.-Y. Jeon, H. K. Lee, K. H. Kim, E.-H. Lee, W.-Y. Oh, B. Y. Kim, H.-W. Lee, and Y. W. Koh, “Harmonically mode-locked fiber laser with an acousto-optic modulator in a Sagnac loop and Faraday rotating mirror cavity,” Opt. Commun. 149, 312–316 (1998).
[Crossref]

F. X. Kärtner, J. Aus der Au, and U. Keller, “Mode-locking with slow and fast saturable absorbers-What’s the difference?” IEEE J. Sel. Top. Quantum Electron. 4, 159–168 (1998).
[Crossref]

1997 (1)

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, Z. Shi, V. Scheuer, M. Tilsch, T. Tschudi, and U. Keller, “Semiconductor saturable absorber mirrors supporting sub-10-fs pulses,” Appl. Phys. B 65, 137–150 (1997).
[Crossref]

1996 (1)

F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 2, 540–556 (1996).
[Crossref]

1988 (1)

M. Nakazawa, K. Suzuki, and H. A. Haus, “Modulational instability oscillation in nonlinear dispersive ring cavity,” Phys. Rev. A 38, 5193–5196 (1988).
[Crossref]

1978 (1)

J. N. Eckstein, A. I. Ferguson, and T. W. Hansch, “High-resolution two-photon spectroscopy with picosecond light pulses,” Phys. Rev. Lett. 40, 847–850 (1978).
[Crossref]

Abramski, K. M.

Agrawal, G. P.

G. P. Agrawal, Applications of Nonlinear Fiber Optics, 2nd ed. (Academic, 2008).

Aus der Au, J.

F. X. Kärtner, J. Aus der Au, and U. Keller, “Mode-locking with slow and fast saturable absorbers-What’s the difference?” IEEE J. Sel. Top. Quantum Electron. 4, 159–168 (1998).
[Crossref]

Bae, M.-K.

Y.-W. Song, S.-Y. Jang, W.-S. Han, and M.-K. Bae, “Graphene mode-lockers for fiber lasers functioned with evanescent field interaction,” Appl. Phys. Lett. 96, 051122 (2010).
[Crossref]

Bale, B. G.

S. K. Truitsyn, B. G. Bale, and M. P. Fedoruk, “Dispersion-managed solitons in fibre systems and lasers,” Phys. Rep. 521, 135–203 (2012).
[Crossref]

Bao, Q.

Y.-H. Lin, C.-Y. Yang, S.-F. Lin, W.-H. Tseng, Q. Bao, C.-I. Wu, and G. R. Lin, “Soliton compression of the erbium-doped fiber laser weakly started mode-locking by nanoscale p-type Bi2Te3 topological insulator particles,” Laser Phys. Lett. 11, 055107 (2014).
[Crossref]

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. Shen, K. P. Loh, and D. Y. Tang, “Atomic layer graphene as saturable absorber for ultrafast pulsed laser,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Basko, D. M.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4, 803–810 (2010).
[Crossref]

Baumgartl, M.

Bonaccorso, F.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4, 803–810 (2010).
[Crossref]

Brodeur, A.

Chang, Y. M.

Y. M. Chang, J. Lee, and J. H. Lee, “Active mode-locking of an erbium-doped fiber laser using an ultrafast silicon-based variable optical attenuator,” Jpn. J. Appl. Phys. 51, 072701 (2012).

Y. M. Chang, H. Kim, J. H. Lee, and Y.-W. Song, “Multilayered graphene efficiently formed by mechanical exfoliation for nonlinear saturable absorbers in fiber mode-locked lasers,” Appl. Phys. Lett. 97, 211102 (2010).
[Crossref]

Chen, S.

Chen, Y.

Choi, S. Y.

S. Y. Choi, H. Jeong, B. H. Hong, F. Rotermund, and D.-I. Yeom, “All-fiber dissipative soliton laser with 10.2  nJ pulse energy using an evanescent field interaction with graphene saturable absorber,” Laser Phys. Lett. 11, 015101 (2014).
[Crossref]

Chong, A.

Chow, K. K.

Clarkson, W. A.

D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives,” J. Opt. Soc. Am. B 27, 63–92 (2010).

Debnath, P.

J. Lee, J. Koo, P. Debnath, Y.-W. Song, and J. H. Lee, “A Q-switched, mode-locked fiber laser using a graphene oxide-based polarization sensitive saturable absorber,” Laser Phys. Lett. 10, 035103 (2013).
[Crossref]

Dutta, N. K.

C. Wu and N. K. Dutta, “High-repetition-rate optical pulse generation using a rational harmonic mode-locked fiber laser,” IEEE J. Quantum Electron. 36, 145–150 (2000).
[Crossref]

Eckstein, J. N.

J. N. Eckstein, A. I. Ferguson, and T. W. Hansch, “High-resolution two-photon spectroscopy with picosecond light pulses,” Phys. Rev. Lett. 40, 847–850 (1978).
[Crossref]

Fedoruk, M.

Fedoruk, M. P.

S. K. Truitsyn, B. G. Bale, and M. P. Fedoruk, “Dispersion-managed solitons in fibre systems and lasers,” Phys. Rep. 521, 135–203 (2012).
[Crossref]

Ferguson, A. I.

J. N. Eckstein, A. I. Ferguson, and T. W. Hansch, “High-resolution two-photon spectroscopy with picosecond light pulses,” Phys. Rev. Lett. 40, 847–850 (1978).
[Crossref]

Ferrari, A. C.

Z. Sun, T. Hasan, and A. C. Ferrari, “Ultrafast lasers mode-locked by nanotubes and graphene,” Physica E 44, 1082–1091 (2012).
[Crossref]

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4, 803–810 (2010).
[Crossref]

Gracia, J. F.

Grange, R.

H. Haiml, R. Grange, and U. Keller, “Optical characterization of semiconductor saturable absorbers,” Appl. Phys. B 79, 331–339 (2004).
[Crossref]

Grodecki, K.

Haiml, H.

H. Haiml, R. Grange, and U. Keller, “Optical characterization of semiconductor saturable absorbers,” Appl. Phys. B 79, 331–339 (2004).
[Crossref]

Han, W.-S.

Y.-W. Song, S.-Y. Jang, W.-S. Han, and M.-K. Bae, “Graphene mode-lockers for fiber lasers functioned with evanescent field interaction,” Appl. Phys. Lett. 96, 051122 (2010).
[Crossref]

Hansch, T. W.

J. N. Eckstein, A. I. Ferguson, and T. W. Hansch, “High-resolution two-photon spectroscopy with picosecond light pulses,” Phys. Rev. Lett. 40, 847–850 (1978).
[Crossref]

Hasan, T.

Z. Sun, T. Hasan, and A. C. Ferrari, “Ultrafast lasers mode-locked by nanotubes and graphene,” Physica E 44, 1082–1091 (2012).
[Crossref]

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4, 803–810 (2010).
[Crossref]

Hasegawa, Y.

Y. Hasegawa and S. Yamashita, “Impact by fiber dispersion, nonlinearity, and saturable absorption in short-cavity mode-locked fiber lasers,” in CLEO 2013, OSA Technical Digest (Optical Society of America, 2013), paper JTu4A.18.

Haus, H. A.

H. A. Haus, “Mode-locking of lasers,” IEEE J. Quantum Electron. 6, 1173–1185 (2000).
[Crossref]

M. Nakazawa, K. Suzuki, and H. A. Haus, “Modulational instability oscillation in nonlinear dispersive ring cavity,” Phys. Rev. A 38, 5193–5196 (1988).
[Crossref]

Herda, R.

Hideur, A.

Hong, B. H.

S. Y. Choi, H. Jeong, B. H. Hong, F. Rotermund, and D.-I. Yeom, “All-fiber dissipative soliton laser with 10.2  nJ pulse energy using an evanescent field interaction with graphene saturable absorber,” Laser Phys. Lett. 11, 015101 (2014).
[Crossref]

Hönninger, C.

Huang, H.

Isomäki, A.

Itoga, E.

Jablonski, M.

Jang, S.-Y.

Y.-W. Song, S.-Y. Jang, W.-S. Han, and M.-K. Bae, “Graphene mode-lockers for fiber lasers functioned with evanescent field interaction,” Appl. Phys. Lett. 96, 051122 (2010).
[Crossref]

Jeon, M.-Y.

M.-Y. Jeon, H. K. Lee, K. H. Kim, E.-H. Lee, W.-Y. Oh, B. Y. Kim, H.-W. Lee, and Y. W. Koh, “Harmonically mode-locked fiber laser with an acousto-optic modulator in a Sagnac loop and Faraday rotating mirror cavity,” Opt. Commun. 149, 312–316 (1998).
[Crossref]

Jeong, H.

S. Y. Choi, H. Jeong, B. H. Hong, F. Rotermund, and D.-I. Yeom, “All-fiber dissipative soliton laser with 10.2  nJ pulse energy using an evanescent field interaction with graphene saturable absorber,” Laser Phys. Lett. 11, 015101 (2014).
[Crossref]

Jeong, M. Y.

Jhon, Y. M.

J. Lee, J. Koo, Y. M. Jhon, and J. H. Lee, “A femtosecond pulse erbium fiber laser incorporating a saturable absorber based on bulk-structured Bi2Te3 topological insulator,” Opt. Express 22, 6156–6173 (2014).

Jung, I. D.

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, Z. Shi, V. Scheuer, M. Tilsch, T. Tschudi, and U. Keller, “Semiconductor saturable absorber mirrors supporting sub-10-fs pulses,” Appl. Phys. B 65, 137–150 (1997).
[Crossref]

F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 2, 540–556 (1996).
[Crossref]

Jung, M.

Kärtner, F. X.

F. X. Kärtner, J. Aus der Au, and U. Keller, “Mode-locking with slow and fast saturable absorbers-What’s the difference?” IEEE J. Sel. Top. Quantum Electron. 4, 159–168 (1998).
[Crossref]

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, Z. Shi, V. Scheuer, M. Tilsch, T. Tschudi, and U. Keller, “Semiconductor saturable absorber mirrors supporting sub-10-fs pulses,” Appl. Phys. B 65, 137–150 (1997).
[Crossref]

F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 2, 540–556 (1996).
[Crossref]

Kataura, H.

Keller, U.

H. Haiml, R. Grange, and U. Keller, “Optical characterization of semiconductor saturable absorbers,” Appl. Phys. B 79, 331–339 (2004).
[Crossref]

C. Hönninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, “Q-switching stability limits of continuous-wave passive mode locking,” J. Opt. Soc. Am. B 16, 46–56 (1999).
[Crossref]

F. X. Kärtner, J. Aus der Au, and U. Keller, “Mode-locking with slow and fast saturable absorbers-What’s the difference?” IEEE J. Sel. Top. Quantum Electron. 4, 159–168 (1998).
[Crossref]

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, Z. Shi, V. Scheuer, M. Tilsch, T. Tschudi, and U. Keller, “Semiconductor saturable absorber mirrors supporting sub-10-fs pulses,” Appl. Phys. B 65, 137–150 (1997).
[Crossref]

F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 2, 540–556 (1996).
[Crossref]

Kim, B. Y.

M.-Y. Jeon, H. K. Lee, K. H. Kim, E.-H. Lee, W.-Y. Oh, B. Y. Kim, H.-W. Lee, and Y. W. Koh, “Harmonically mode-locked fiber laser with an acousto-optic modulator in a Sagnac loop and Faraday rotating mirror cavity,” Opt. Commun. 149, 312–316 (1998).
[Crossref]

Kim, C.-S.

Kim, H.

Y. M. Chang, H. Kim, J. H. Lee, and Y.-W. Song, “Multilayered graphene efficiently formed by mechanical exfoliation for nonlinear saturable absorbers in fiber mode-locked lasers,” Appl. Phys. Lett. 97, 211102 (2010).
[Crossref]

Kim, K. H.

M.-Y. Jeon, H. K. Lee, K. H. Kim, E.-H. Lee, W.-Y. Oh, B. Y. Kim, H.-W. Lee, and Y. W. Koh, “Harmonically mode-locked fiber laser with an acousto-optic modulator in a Sagnac loop and Faraday rotating mirror cavity,” Opt. Commun. 149, 312–316 (1998).
[Crossref]

Koh, Y. W.

M.-Y. Jeon, H. K. Lee, K. H. Kim, E.-H. Lee, W.-Y. Oh, B. Y. Kim, H.-W. Lee, and Y. W. Koh, “Harmonically mode-locked fiber laser with an acousto-optic modulator in a Sagnac loop and Faraday rotating mirror cavity,” Opt. Commun. 149, 312–316 (1998).
[Crossref]

Koo, J.

M. Jung, J. Lee, J. Koo, J. Park, Y.-W. Song, K. Lee, S. Lee, and J. H. Lee, “A femtosecond pulse fiber laser at 1935  nm using a bulk-structured Bi2Te3 topological insulator,” Opt. Express 22, 7865–7874 (2014).
[Crossref]

J. Lee, J. Koo, Y. M. Jhon, and J. H. Lee, “A femtosecond pulse erbium fiber laser incorporating a saturable absorber based on bulk-structured Bi2Te3 topological insulator,” Opt. Express 22, 6156–6173 (2014).

J. Lee, J. Koo, P. Debnath, Y.-W. Song, and J. H. Lee, “A Q-switched, mode-locked fiber laser using a graphene oxide-based polarization sensitive saturable absorber,” Laser Phys. Lett. 10, 035103 (2013).
[Crossref]

Lecaplain, C.

Lee, E.-H.

M.-Y. Jeon, H. K. Lee, K. H. Kim, E.-H. Lee, W.-Y. Oh, B. Y. Kim, H.-W. Lee, and Y. W. Koh, “Harmonically mode-locked fiber laser with an acousto-optic modulator in a Sagnac loop and Faraday rotating mirror cavity,” Opt. Commun. 149, 312–316 (1998).
[Crossref]

Lee, H. D.

Lee, H. K.

M.-Y. Jeon, H. K. Lee, K. H. Kim, E.-H. Lee, W.-Y. Oh, B. Y. Kim, H.-W. Lee, and Y. W. Koh, “Harmonically mode-locked fiber laser with an acousto-optic modulator in a Sagnac loop and Faraday rotating mirror cavity,” Opt. Commun. 149, 312–316 (1998).
[Crossref]

Lee, H.-W.

M.-Y. Jeon, H. K. Lee, K. H. Kim, E.-H. Lee, W.-Y. Oh, B. Y. Kim, H.-W. Lee, and Y. W. Koh, “Harmonically mode-locked fiber laser with an acousto-optic modulator in a Sagnac loop and Faraday rotating mirror cavity,” Opt. Commun. 149, 312–316 (1998).
[Crossref]

Lee, J.

M. Jung, J. Lee, J. Koo, J. Park, Y.-W. Song, K. Lee, S. Lee, and J. H. Lee, “A femtosecond pulse fiber laser at 1935  nm using a bulk-structured Bi2Te3 topological insulator,” Opt. Express 22, 7865–7874 (2014).
[Crossref]

J. Lee, J. Koo, Y. M. Jhon, and J. H. Lee, “A femtosecond pulse erbium fiber laser incorporating a saturable absorber based on bulk-structured Bi2Te3 topological insulator,” Opt. Express 22, 6156–6173 (2014).

J. Lee, J. Koo, P. Debnath, Y.-W. Song, and J. H. Lee, “A Q-switched, mode-locked fiber laser using a graphene oxide-based polarization sensitive saturable absorber,” Laser Phys. Lett. 10, 035103 (2013).
[Crossref]

Y. M. Chang, J. Lee, and J. H. Lee, “Active mode-locking of an erbium-doped fiber laser using an ultrafast silicon-based variable optical attenuator,” Jpn. J. Appl. Phys. 51, 072701 (2012).

Lee, J. H.

M. Jung, J. Lee, J. Koo, J. Park, Y.-W. Song, K. Lee, S. Lee, and J. H. Lee, “A femtosecond pulse fiber laser at 1935  nm using a bulk-structured Bi2Te3 topological insulator,” Opt. Express 22, 7865–7874 (2014).
[Crossref]

J. Lee, J. Koo, Y. M. Jhon, and J. H. Lee, “A femtosecond pulse erbium fiber laser incorporating a saturable absorber based on bulk-structured Bi2Te3 topological insulator,” Opt. Express 22, 6156–6173 (2014).

J. Lee, J. Koo, P. Debnath, Y.-W. Song, and J. H. Lee, “A Q-switched, mode-locked fiber laser using a graphene oxide-based polarization sensitive saturable absorber,” Laser Phys. Lett. 10, 035103 (2013).
[Crossref]

Y. M. Chang, J. Lee, and J. H. Lee, “Active mode-locking of an erbium-doped fiber laser using an ultrafast silicon-based variable optical attenuator,” Jpn. J. Appl. Phys. 51, 072701 (2012).

H. D. Lee, J. H. Lee, M. Y. Jeong, and C.-S. Kim, “Characterization of wavelength-swept active mode locking fiber laser based on reflective semiconductor optical amplifier,” Opt. Express 19, 14586–14593 (2011).
[Crossref]

Y. M. Chang, H. Kim, J. H. Lee, and Y.-W. Song, “Multilayered graphene efficiently formed by mechanical exfoliation for nonlinear saturable absorbers in fiber mode-locked lasers,” Appl. Phys. Lett. 97, 211102 (2010).
[Crossref]

Lee, K.

Lee, S.

Lin, G. R.

Y.-H. Lin, C.-Y. Yang, S.-F. Lin, W.-H. Tseng, Q. Bao, C.-I. Wu, and G. R. Lin, “Soliton compression of the erbium-doped fiber laser weakly started mode-locking by nanoscale p-type Bi2Te3 topological insulator particles,” Laser Phys. Lett. 11, 055107 (2014).
[Crossref]

Lin, S.-F.

Y.-H. Lin, C.-Y. Yang, S.-F. Lin, W.-H. Tseng, Q. Bao, C.-I. Wu, and G. R. Lin, “Soliton compression of the erbium-doped fiber laser weakly started mode-locking by nanoscale p-type Bi2Te3 topological insulator particles,” Laser Phys. Lett. 11, 055107 (2014).
[Crossref]

Lin, Y.-H.

Y.-H. Lin, C.-Y. Yang, S.-F. Lin, W.-H. Tseng, Q. Bao, C.-I. Wu, and G. R. Lin, “Soliton compression of the erbium-doped fiber laser weakly started mode-locking by nanoscale p-type Bi2Te3 topological insulator particles,” Laser Phys. Lett. 11, 055107 (2014).
[Crossref]

Liu, H. H.

Loh, K. P.

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. Shen, K. P. Loh, and D. Y. Tang, “Atomic layer graphene as saturable absorber for ultrafast pulsed laser,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Lu, S.

Marcherzynski, W.

Martinez, A.

A. Martinez and S. Yamashita, “10  GHz fundamental mode fiber laser using a graphene saturable absorber,” Appl. Phys. Lett. 101, 041118 (2012).
[Crossref]

A. Martinez and S. Yamashita, “Multi-gigahertz repetition rate passively mode locked fiber lasers using carbon nanotubes,” Opt. Express 19, 6155–6163 (2011).
[Crossref]

Matuschek, N.

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, Z. Shi, V. Scheuer, M. Tilsch, T. Tschudi, and U. Keller, “Semiconductor saturable absorber mirrors supporting sub-10-fs pulses,” Appl. Phys. B 65, 137–150 (1997).
[Crossref]

Mazur, E.

Morier-Genoud, F.

C. Hönninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, “Q-switching stability limits of continuous-wave passive mode locking,” J. Opt. Soc. Am. B 16, 46–56 (1999).
[Crossref]

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, Z. Shi, V. Scheuer, M. Tilsch, T. Tschudi, and U. Keller, “Semiconductor saturable absorber mirrors supporting sub-10-fs pulses,” Appl. Phys. B 65, 137–150 (1997).
[Crossref]

Moser, M.

Nakazawa, M.

M. Nakazawa, K. Suzuki, and H. A. Haus, “Modulational instability oscillation in nonlinear dispersive ring cavity,” Phys. Rev. A 38, 5193–5196 (1988).
[Crossref]

Ni, Z.

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. Shen, K. P. Loh, and D. Y. Tang, “Atomic layer graphene as saturable absorber for ultrafast pulsed laser,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Nilsson, J.

D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives,” J. Opt. Soc. Am. B 27, 63–92 (2010).

Nishizawa, N.

Nozaki, Y.

Oh, W.-Y.

M.-Y. Jeon, H. K. Lee, K. H. Kim, E.-H. Lee, W.-Y. Oh, B. Y. Kim, H.-W. Lee, and Y. W. Koh, “Harmonically mode-locked fiber laser with an acousto-optic modulator in a Sagnac loop and Faraday rotating mirror cavity,” Opt. Commun. 149, 312–316 (1998).
[Crossref]

Okhotnikov, O.

Okhotnikov, O. G.

Paletko, P.

Park, J.

Paschotta, R.

Popa, D.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4, 803–810 (2010).
[Crossref]

Premaratne, M.

K. Song and M. Premaratne, “Effects of SPM, XPM, and four-wave-mixing in L-band EDFAs on fiber-optic signal transmission,” IEEE Photon. Technol. Lett. 12, 1630–1632 (2000).
[Crossref]

Privitera, G.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4, 803–810 (2010).
[Crossref]

Renninger, W. H.

Richardson, D. J.

D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives,” J. Opt. Soc. Am. B 27, 63–92 (2010).

Rotermund, F.

S. Y. Choi, H. Jeong, B. H. Hong, F. Rotermund, and D.-I. Yeom, “All-fiber dissipative soliton laser with 10.2  nJ pulse energy using an evanescent field interaction with graphene saturable absorber,” Laser Phys. Lett. 11, 015101 (2014).
[Crossref]

Sakakibara, Y.

Schaffer, C. B.

Scheuer, V.

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, Z. Shi, V. Scheuer, M. Tilsch, T. Tschudi, and U. Keller, “Semiconductor saturable absorber mirrors supporting sub-10-fs pulses,” Appl. Phys. B 65, 137–150 (1997).
[Crossref]

Schreiber, T.

Set, S. Y.

Shen, Z.

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. Shen, K. P. Loh, and D. Y. Tang, “Atomic layer graphene as saturable absorber for ultrafast pulsed laser,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Shi, Z.

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, Z. Shi, V. Scheuer, M. Tilsch, T. Tschudi, and U. Keller, “Semiconductor saturable absorber mirrors supporting sub-10-fs pulses,” Appl. Phys. B 65, 137–150 (1997).
[Crossref]

Shtyrina, O.

Sobon, G.

Song, K.

K. Song and M. Premaratne, “Effects of SPM, XPM, and four-wave-mixing in L-band EDFAs on fiber-optic signal transmission,” IEEE Photon. Technol. Lett. 12, 1630–1632 (2000).
[Crossref]

Song, Y.-W.

M. Jung, J. Lee, J. Koo, J. Park, Y.-W. Song, K. Lee, S. Lee, and J. H. Lee, “A femtosecond pulse fiber laser at 1935  nm using a bulk-structured Bi2Te3 topological insulator,” Opt. Express 22, 7865–7874 (2014).
[Crossref]

J. Lee, J. Koo, P. Debnath, Y.-W. Song, and J. H. Lee, “A Q-switched, mode-locked fiber laser using a graphene oxide-based polarization sensitive saturable absorber,” Laser Phys. Lett. 10, 035103 (2013).
[Crossref]

Y. M. Chang, H. Kim, J. H. Lee, and Y.-W. Song, “Multilayered graphene efficiently formed by mechanical exfoliation for nonlinear saturable absorbers in fiber mode-locked lasers,” Appl. Phys. Lett. 97, 211102 (2010).
[Crossref]

Y.-W. Song, S.-Y. Jang, W.-S. Han, and M.-K. Bae, “Graphene mode-lockers for fiber lasers functioned with evanescent field interaction,” Appl. Phys. Lett. 96, 051122 (2010).
[Crossref]

Sotor, J.

Sun, Z.

Z. Sun, T. Hasan, and A. C. Ferrari, “Ultrafast lasers mode-locked by nanotubes and graphene,” Physica E 44, 1082–1091 (2012).
[Crossref]

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4, 803–810 (2010).
[Crossref]

Sutter, D. H.

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, Z. Shi, V. Scheuer, M. Tilsch, T. Tschudi, and U. Keller, “Semiconductor saturable absorber mirrors supporting sub-10-fs pulses,” Appl. Phys. B 65, 137–150 (1997).
[Crossref]

Suzuki, K.

M. Nakazawa, K. Suzuki, and H. A. Haus, “Modulational instability oscillation in nonlinear dispersive ring cavity,” Phys. Rev. A 38, 5193–5196 (1988).
[Crossref]

Tanaka, Y.

Tang, D.

Tang, D. Y.

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. Shen, K. P. Loh, and D. Y. Tang, “Atomic layer graphene as saturable absorber for ultrafast pulsed laser,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Tang, P.

Tilsch, M.

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, Z. Shi, V. Scheuer, M. Tilsch, T. Tschudi, and U. Keller, “Semiconductor saturable absorber mirrors supporting sub-10-fs pulses,” Appl. Phys. B 65, 137–150 (1997).
[Crossref]

Torrisi, F.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4, 803–810 (2010).
[Crossref]

Truitsyn, S. K.

S. K. Truitsyn, B. G. Bale, and M. P. Fedoruk, “Dispersion-managed solitons in fibre systems and lasers,” Phys. Rep. 521, 135–203 (2012).
[Crossref]

Tschudi, T.

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, Z. Shi, V. Scheuer, M. Tilsch, T. Tschudi, and U. Keller, “Semiconductor saturable absorber mirrors supporting sub-10-fs pulses,” Appl. Phys. B 65, 137–150 (1997).
[Crossref]

Tseng, W.-H.

Y.-H. Lin, C.-Y. Yang, S.-F. Lin, W.-H. Tseng, Q. Bao, C.-I. Wu, and G. R. Lin, “Soliton compression of the erbium-doped fiber laser weakly started mode-locking by nanoscale p-type Bi2Te3 topological insulator particles,” Laser Phys. Lett. 11, 055107 (2014).
[Crossref]

Turitsyn, S.

Wang, F.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4, 803–810 (2010).
[Crossref]

Wang, Y.

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. Shen, K. P. Loh, and D. Y. Tang, “Atomic layer graphene as saturable absorber for ultrafast pulsed laser,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Wang, Z.

Wen, S.

Wise, F. W.

Wu, C.

C. Wu and N. K. Dutta, “High-repetition-rate optical pulse generation using a rational harmonic mode-locked fiber laser,” IEEE J. Quantum Electron. 36, 145–150 (2000).
[Crossref]

Wu, C.-I.

Y.-H. Lin, C.-Y. Yang, S.-F. Lin, W.-H. Tseng, Q. Bao, C.-I. Wu, and G. R. Lin, “Soliton compression of the erbium-doped fiber laser weakly started mode-locking by nanoscale p-type Bi2Te3 topological insulator particles,” Laser Phys. Lett. 11, 055107 (2014).
[Crossref]

Yaguchi, H.

Yamashita, S.

A. Martinez and S. Yamashita, “10  GHz fundamental mode fiber laser using a graphene saturable absorber,” Appl. Phys. Lett. 101, 041118 (2012).
[Crossref]

A. Martinez and S. Yamashita, “Multi-gigahertz repetition rate passively mode locked fiber lasers using carbon nanotubes,” Opt. Express 19, 6155–6163 (2011).
[Crossref]

Y. Hasegawa and S. Yamashita, “Impact by fiber dispersion, nonlinearity, and saturable absorption in short-cavity mode-locked fiber lasers,” in CLEO 2013, OSA Technical Digest (Optical Society of America, 2013), paper JTu4A.18.

Yan, Y.

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. Shen, K. P. Loh, and D. Y. Tang, “Atomic layer graphene as saturable absorber for ultrafast pulsed laser,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Yang, C.-Y.

Y.-H. Lin, C.-Y. Yang, S.-F. Lin, W.-H. Tseng, Q. Bao, C.-I. Wu, and G. R. Lin, “Soliton compression of the erbium-doped fiber laser weakly started mode-locking by nanoscale p-type Bi2Te3 topological insulator particles,” Laser Phys. Lett. 11, 055107 (2014).
[Crossref]

Yeom, D.-I.

S. Y. Choi, H. Jeong, B. H. Hong, F. Rotermund, and D.-I. Yeom, “All-fiber dissipative soliton laser with 10.2  nJ pulse energy using an evanescent field interaction with graphene saturable absorber,” Laser Phys. Lett. 11, 015101 (2014).
[Crossref]

Zhang, H.

Zhao, C.

Zou, Y.

ACS Nano (1)

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4, 803–810 (2010).
[Crossref]

Adv. Funct. Mater. (1)

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. Shen, K. P. Loh, and D. Y. Tang, “Atomic layer graphene as saturable absorber for ultrafast pulsed laser,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Appl. Phys. B (2)

H. Haiml, R. Grange, and U. Keller, “Optical characterization of semiconductor saturable absorbers,” Appl. Phys. B 79, 331–339 (2004).
[Crossref]

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, Z. Shi, V. Scheuer, M. Tilsch, T. Tschudi, and U. Keller, “Semiconductor saturable absorber mirrors supporting sub-10-fs pulses,” Appl. Phys. B 65, 137–150 (1997).
[Crossref]

Appl. Phys. Lett. (3)

A. Martinez and S. Yamashita, “10  GHz fundamental mode fiber laser using a graphene saturable absorber,” Appl. Phys. Lett. 101, 041118 (2012).
[Crossref]

Y.-W. Song, S.-Y. Jang, W.-S. Han, and M.-K. Bae, “Graphene mode-lockers for fiber lasers functioned with evanescent field interaction,” Appl. Phys. Lett. 96, 051122 (2010).
[Crossref]

Y. M. Chang, H. Kim, J. H. Lee, and Y.-W. Song, “Multilayered graphene efficiently formed by mechanical exfoliation for nonlinear saturable absorbers in fiber mode-locked lasers,” Appl. Phys. Lett. 97, 211102 (2010).
[Crossref]

IEEE J. Quantum Electron. (2)

C. Wu and N. K. Dutta, “High-repetition-rate optical pulse generation using a rational harmonic mode-locked fiber laser,” IEEE J. Quantum Electron. 36, 145–150 (2000).
[Crossref]

H. A. Haus, “Mode-locking of lasers,” IEEE J. Quantum Electron. 6, 1173–1185 (2000).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

F. X. Kärtner, J. Aus der Au, and U. Keller, “Mode-locking with slow and fast saturable absorbers-What’s the difference?” IEEE J. Sel. Top. Quantum Electron. 4, 159–168 (1998).
[Crossref]

F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 2, 540–556 (1996).
[Crossref]

IEEE Photon. Technol. Lett. (1)

K. Song and M. Premaratne, “Effects of SPM, XPM, and four-wave-mixing in L-band EDFAs on fiber-optic signal transmission,” IEEE Photon. Technol. Lett. 12, 1630–1632 (2000).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (4)

Jpn. J. Appl. Phys. (1)

Y. M. Chang, J. Lee, and J. H. Lee, “Active mode-locking of an erbium-doped fiber laser using an ultrafast silicon-based variable optical attenuator,” Jpn. J. Appl. Phys. 51, 072701 (2012).

Laser Phys. Lett. (3)

S. Y. Choi, H. Jeong, B. H. Hong, F. Rotermund, and D.-I. Yeom, “All-fiber dissipative soliton laser with 10.2  nJ pulse energy using an evanescent field interaction with graphene saturable absorber,” Laser Phys. Lett. 11, 015101 (2014).
[Crossref]

Y.-H. Lin, C.-Y. Yang, S.-F. Lin, W.-H. Tseng, Q. Bao, C.-I. Wu, and G. R. Lin, “Soliton compression of the erbium-doped fiber laser weakly started mode-locking by nanoscale p-type Bi2Te3 topological insulator particles,” Laser Phys. Lett. 11, 055107 (2014).
[Crossref]

J. Lee, J. Koo, P. Debnath, Y.-W. Song, and J. H. Lee, “A Q-switched, mode-locked fiber laser using a graphene oxide-based polarization sensitive saturable absorber,” Laser Phys. Lett. 10, 035103 (2013).
[Crossref]

Opt. Commun. (1)

M.-Y. Jeon, H. K. Lee, K. H. Kim, E.-H. Lee, W.-Y. Oh, B. Y. Kim, H.-W. Lee, and Y. W. Koh, “Harmonically mode-locked fiber laser with an acousto-optic modulator in a Sagnac loop and Faraday rotating mirror cavity,” Opt. Commun. 149, 312–316 (1998).
[Crossref]

Opt. Express (8)

J. Lee, J. Koo, Y. M. Jhon, and J. H. Lee, “A femtosecond pulse erbium fiber laser incorporating a saturable absorber based on bulk-structured Bi2Te3 topological insulator,” Opt. Express 22, 6156–6173 (2014).

A. Isomäki and O. G. Okhotnikov, “All-fiber ytterbium soliton mode-locked laser with dispersion control by solid-core photonic bandgap fiber,” Opt. Express 14, 4368–4373 (2006).
[Crossref]

A. Martinez and S. Yamashita, “Multi-gigahertz repetition rate passively mode locked fiber lasers using carbon nanotubes,” Opt. Express 19, 6155–6163 (2011).
[Crossref]

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Figures (9)

Fig. 1.
Fig. 1.

Example of a transmission curve for a saturable absorber.

Fig. 2.
Fig. 2.

Schematic of the mode-locked fiber laser with a saturable absorber used for this numerical simulation.

Fig. 3.
Fig. 3.

Total cavity length and fundamental resonance frequency versus net cavity GVD β ( 2 ) .

Fig. 4.
Fig. 4.

Calculated minimum modulation depth of a saturable absorber as a function of the net cavity GVD β ( 2 ) , which is required to generate stable mode-locked pulses from a fiberized cavity.

Fig. 5.
Fig. 5.

(a) Change in the temporal shape of the output pulses calculated with an increase in the modulation depth at a specific net cavity GVD of 0.2 ps 2 . (b) Temporal width of the output pulses calculated as a function of modulation depth.

Fig. 6.
Fig. 6.

(a) Change in the spectral shape of the output pulses calculated according to the increase in the modulation depth at a specific net cavity GVD of 0.2 ps 2 . (b) 3 dB bandwidth calculated as a function of the modulation depth. (c) Time-bandwidth product of the output pulses as a function of the modulation depth.

Fig. 7.
Fig. 7.

(a) Output pulse width, obtainable with the minimum modulation depth required for each net cavity GVD value. (b) 3 dB spectral bandwidth of the output pulses. (c) Time-bandwidth product of the output pulses.

Fig. 8.
Fig. 8.

(a) Minimum modulation depth required for a saturable absorber with various χ ( 3 ) nonlinearity γ values for the SMF, DCF, and EDF used in a laser cavity. (b) Temporal width of the output pulses calculated for the conditions where a saturable absorber with the required modulation depth is used in the cavity.

Fig. 9.
Fig. 9.

(a) Minimum modulation depth required for a saturable absorber as a function of the net cavity GVD for three different saturation gain levels of 2, 3, and 4 pJ. (b) Temporal width of the output pulses calculated when a saturable absorber with the required modulation depth is used in the cavity.

Tables (1)

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Table 1. Fiber Parameters Used for the Simulation [34] a

Equations (3)

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T ( I ) = 1 Δ T · exp ( I I sat ) α ns ,
A ( z , τ ) z + i 2 ( β ( 2 ) + i g 1 Ω f 2 ) 2 A ( z , τ ) τ 2 = g 2 A ( z , τ ) + β ( 3 ) 6 3 A ( z , τ ) τ 3 + i γ | A ( z , τ ) | 2 A ( z , τ ) ,
g = g 0 / ( 1 + E / E sat _ gain ) ,

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